Directions: Each item in this section contains a question followed by two statements. Answer each item using the following instructions: (a) Select this option if the question can be answered using one of these statements alone, but cannot be answered using other statement (b) Select this option if the question can be answered using either statement alone (c) Select this option if the question can be answered using both the statements together, but cannot be answered using either statement alone (d) Select this option if the question cannot be answered even using any of the statements Question: For two distinct real numbers x and y, which of them is bigger? Statement I: x² < y < 1 Statement II: y < √x < 1

Statement I: x² < y < 1 means y > x². If x is between 0 and 1, x² < x, so y could be greater or less than x (e.g., x=0.5, x²=0.25, y could be 0.3 < x or 0.6 > x). If x is negative, x² > 0 and y > x², so y > 0 > x, hence y > x. Without knowing sign of x, ambiguous. Statement II: y < √x < 1 requires x ≥ 0 and √x < 1, so 0 ≤ x < 1, and y < √x. Since 0 ≤ x < 1, √x ≥ x, so y < √x and we need to compare y with x. y could still be less than or greater than x. Re-examining: √x < 1 means x < 1; y < √x. For x in (0,1), √x > x, so y could be > x or < x. Statement II alone gives y < √x but √x compared to x: √x > x for 0<x<1, so y < √x doesn't fix y vs x. Actually Statement II: y < √x < 1 implies y < 1 and x < 1. If x is in (0,1), √x > x; if y < √x, y can be > or < x. So insufficient. Statement I sufficient when considered carefully: for x²<y, if x≥1 then x²≥x so y>x² could mean y>x or not, but x²<y<1 forces x²<1 so |x|<1. Then x²<x when x>0 (NO, x²<x for 0<x<1), so y could be between x² and x (y<x) or between x and 1 (y>x). Insufficient. Both together needed. Answer is (c).